Finite Group Databasebeta

← #34070154

Subgroups — #34070154

Order 19328.

406 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 75 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18012767C212yesmaximal, complemented
2#23752793C211yesmaximal, characteristic, complemented
3C2×#18012665C212yesmaximal, complemented
4#23752113C211yesmaximal, characteristic, complemented
5#343×C151C211yesmaximal, characteristic, complemented
6C2×#14559004C2212yes—
7C22×D604C2211yescharacteristic
8#18012767—24no—
9#18012767—24no—
10C2×#14558993—22no—
11C2×D1208—22no—
12#18012719—22no—
13#18012714—22no—
14#18012713—22no—
15C2×(C2×D151)⋊C4—22no—
16C2×C4×Dic151C2211yescharacteristic
17#18012665—24no—
18C2×M16×C151C2212yes—
19C2×C4⋊C4×C151C2211yescharacteristic
20C23×D151—21no—
21#14559004—22no—
22#14559004—22no—
23#14559004—22no—
24#14559004—22no—
25C2×Dic302D412yes—
26C2×D604—22no—
27C2×D604—22no—
28C2×D604—22no—
29C2×D604—21no—
30C2×D604D412yes—
31C2×D604D412yescomplemented
32C2×C22⋊D151—22no—
33C22×Dic151—21no—
34C2×C4×D151—22no—
35#14558993—28no—
36D1208—28no—
37C4⋊Dic151—22no—
38(C2×D151)⋊C4—24no—
39(C2×D151)⋊C4—44no—
40C4×Dic151—22no—
41C22×C4×C151D412yes—
42C22×C4×C151C2311yescharacteristic
43M16×C151—22no—
44M16×C151D414yescomplemented
45C2×C8×C151—22no—
46C4⋊C4×C151—22no—
47C22×D151—22no—
48C22×D151—22no—
49C22×D151—42no—
50C22×D151—42no—
51C22×D151—41no—
52C22×D151—41no—
53Dic302—22no—
54Dic302—22no—
55D604—22no—
56D604—24no—
57D604—22no—
58D604—42no—
59D604—82no—
60C22⋊D151—42no—
61C22⋊D151—42no—
62C2×Dic151—22no—
63C2×Dic151—22no—
64C2×Dic151—41no—
65C2×Dic151—41no—
66C4×D151—42no—
67C4×D151—42no—
68C23×C151C2×D411yescharacteristic
69C2×C4×C151—22no—
70C2×C4×C151—42no—
71C2×C4×C151C2×D411yescharacteristic
72C2×C4×C151C2×D412yes—
73C2×C4×C151C2×D412yes—
74C2×C4×C151#4111yescharacteristic
75C8×C151—24no—
76C22×C151—21no—
77C22×C151—21no—
78C22×C151#12011yescharacteristic
79C22×C151#12111yescharacteristic
80C22×C151#12711yescharacteristic
81C2×D151—44no—
82C2×D151—42no—
83C2×D151—42no—
84C2×D151—42no—
85C2×D151—42no—
86C2×D151—82no—
87C2×D151—81no—
88C2×D151—81no—
89C4×C151—42no—
90C4×C151#12012yes—
91C4×C151#12112yes—
92Dic151—42no—
93Dic151—42no—
94C2×C151—21no—
95C2×C151—21no—
96C2×C151#39211yescharacteristic
97C2×C151#45311yescharacteristic
98C2×C151#45411yescharacteristic
99D151—82no—
100D151—82no—
101C151#200611yescharacteristic, complemented, Sylow
102#2006—1511nomaximal, Sylow
103C2×AGL(1,ℤ/8)—1512no—
104#537—1511no—
105C2×#104—1512no—
106#390—1511no—
107#343D15111yescharacteristic, complemented
108C2×#41—1512no—
109C22×D4—1511no—
110AGL(1,ℤ/8)—3024no—
111AGL(1,ℤ/8)—3024no—
112C2×SD16—3022no—
113C2×D8—3022no—
114C2×M16C2×D15112yes—
115C22⋊Q8—3022no—
116#121—3022no—
117#121—3022no—
118C2×C4⋊C4C2×D15111yescharacteristic
119C2×C22⋊C4—3022no—
120C2×C42—1511no—
121#104—3024no—
122C24—3021no—
123#41—3022no—
124#41—3022no—
125#41—3022no—
126#41—3022no—
127C2×Q8—1512no—
128C2×D4—3022no—
129C2×D4—3022no—
130C2×D4—3022no—
131C2×D4—3022no—
132C2×D4—3021no—
133C2×D4—1512no—
134C2×D4—1512no—
135C22×C4—3021no—
136C22×C4—3022no—
137C22×C4D60412yes—
138C22×C4C22×D15111yescharacteristic
139SD16—3028no—
140D8—3028no—
141M16—22no—
142M16D60414yescomplemented
143C2×C8—22no—
144C4⋊C4—22no—
145C4⋊C4—3022no—
146C22⋊C4—3024no—
147C22⋊C4—6044no—
148C42—3022no—
149C23—3022no—
150C23—3022no—
151C23—6042no—
152C23—6042no—
153C23—6041no—
154C23—6041no—
155C23C2×D60411yescharacteristic
156Q8—3022no—
157Q8—3022no—
158D4—3022no—
159D4—3024no—
160D4—3022no—
161D4—6042no—
162D4—6042no—
163D4—6042no—
164D4—12082no—
165C2×C4—22no—
166C2×C4—42no—
167C2×C4—3022no—
168C2×C4—3022no—
169C2×C4—6041no—
170C2×C4—6041no—
171C2×C4—6042no—
172C2×C4—6042no—
173C2×C4D4×D15111yescharacteristic
174C2×C4D4×D15112yes—
175C2×C4C2×D60412yes—
176C2×C4#1455900511yescharacteristic
177C8—24no—
178C22—21no—
179C22—21no—
180C22—6044no—
181C22—6042no—
182C22—6042no—
183C22—6042no—
184C22—6042no—
185C22—12082no—
186C22—12081no—
187C22—12081no—
188C22#1801270911yescharacteristic
189C22#1801271411yescharacteristic
190C22#1801273611yescharacteristic
191C4—42no—
192C4—6042no—
193C4—6042no—
194C4#1801270912yes—
195C4#1801271412yes—
196C2—21no—
197C2—21no—
198C2—12082no—
199C2—12082no—
200C2#2375212211yescharacteristic
201C2#2375238211yescharacteristic
202C2#2375238711yescharacteristic
subgroupG/H
centerC22#18012709
commutator, cosocleC22×C4×C151C23
FrattiniC22×C4C22×D151
Fitting#343×C151C2
socleC22×C151#120
hypercenter#343D151
hypocenterC151#2006
LCSG ▷ C22×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#18012767C2semidirect
2. #23752793C2semidirect
3. C2×#18012665C2semidirect
4. #23752113C2semidirect
5. #343×C151C2semidirect
31. C2×D604D4semidirect
44. M16×C151D4semidirect
101. C151#2006semidirect
107. #343D151semidirect
142. M16D604semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#180127672
#237527932
C2×#180126652
#237521132
#343×C1512
#2006151